An airplane is flying at a constant speed of 500 mph at a bearing of 45° north of west. A 40 mph wind is blowing due south. What are the plane's actual speed and direction? Draw a diagram and show your work to justify your answer. Round the speed to the nearest tenth and the direction to the nearest degree. (5 points)
Answers
Answer:I’m pretty sure I got this one right too
Step-by-step explanation:
The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.
What are the x and y-components of a vector?"In a two-dimensional coordinate system, any vector can be broken into x -component and y -component according to axis."
We can assume, east as the positive x- axis and north as the positive y-axis, respectively.
Similarly, west as the negative x- and south as the negative y-axis, respectively.
Therefore, the x- and y-components of the speeds.
Now, for the airplane:
x-component: - 500 × cos(45°) mph = - 353.55 mph
y-component: 500 × sin(45°) mph = 353.55 mph
For the wind:
y-component: -40 mph
Therefore, sum of the x-components = -353.55 mph
Similarly, sum of the y-components = (353.55 - 40) mph = 313.55 mph
Now, the actual speed =
[tex]\sqrt{(-353.55)^{2} + (313.55)^{2}}[/tex] mph
= [tex]\sqrt{223313.6}[/tex] mph
= 472.56 mph
Now, the direction of the airplane is:
tan(Ф) = [tex]\frac{313.55}{- 353.55}[/tex]
⇒ Ф = tan⁻¹( [tex]\frac{313.55}{- 353.55}[/tex])
⇒ Ф = - 41.57°
The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.
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Related Questions
Part E
Open the parallel lines rotation application .The right set of parallel lines is a 90° rotation counterclockwise of the left set of
parallel lines. Click the 90° counterclockwise button. Are the two sets of parallel lines the same? What does this mean about
how parallel lines change when you rotate them?
Answers
Two sets of parallel lines continue to stay equidistant to each other in each set of parallel lines, this same parallel line at an angle to the Y-axis will not intersect the parallel line at an angle to the x-axis if they are extended infinitely.
What is Angle Translation?A translation is a type of transformation that involves sliding each point in a figure the same distance in the same direction. In geometry, translating something simply means moving it around. We do not alter it in any way. When we translate a segment, it remains a segment and its length remains constant. Similarly, when we translate an angle, the angle's measure remains constant.According to the given diagram:
Although the two sets of parallel lines in each set remain equidistant to each other, the parallel line at an angle to the Y-axis will not intersect the parallel line at an angle to the x-axis if they are extended infinitely.Therefore, two sets of parallel lines continue to stay equidistant to each other in each set of parallel lines, this same parallel line at an angle to the Y-axis will not intersect the parallel line at an angle to the x-axis if they are extended infinitely.
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Use the information to answer the question.
Consider the triangle.
16x + 5
4x + 2
8x + 1
Part A
Which expression represents the perimeter of the triangle?
Answers
Answer:
13x^8 + 4x^5 - 16x^2 try this
Step-by-step explanation:
What 5 points are not coplanar with H, E, and A?
Answers
5 points that are not coplanar with H, E, and A are B, I, C, F, and G.
The figure in the given diagram is a cube. We have to find the 5 points in the cube that are not coplanar with H, E, and A.
Points are non-coplanar if they don't lie on the same plane.
From the given cube diagram, it is clear points A, E, H, J, and D lie on the same plane, while the points B, I, C, F, and G lie on a different plane. Since we have to check if the points are coplanar with respect to the given points H, E, and A.
It can be concluded that points J and D are coplanar with the given points H, E, and A as they all lie in the same plane, while the points B, I, C, F, and G are non coplanar points with respect to the given points H, E, and A as they lie on a different plane.
Therefore, using the concept of coplanar and non coplanar points, we get 5 points that are not coplanar with H, E, and A as B, I, C, F, and G.
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Can someone tell me how to solve this? Thank you
Answers
Answer:
domain: all real numbers except x=3 and x=5.
Step-by-step explanation:
You want the domain of a composition of rational functions f(x)=1/(x-2) and g(x)=4/(x-3).
DomainThe domain of a function is the set of values of the independent variable for which the function is defined.
To compute f(g(x)), you must first compute g(x). When x=3, the denominator of the function 4/(x-3) is zero, so the value is undefined. The domain must exclude x=3.
The composition is found by substituting g(x) for x in the definition of f(x).
[tex]f(g(x)) = f(\dfrac{4}{x-3}) =\dfrac{1}{\dfrac{4}{x-3}-2}=\dfrac{x-3}{4-2(x-3)}\\\\f(g(x))=\dfrac{x-3}{4-2x+6}=\dfrac{x-3}{2(5-x)}[/tex]
We have written the composition in this form so you can see there is a denominator factor that will be zero when x=5. The domain of f(g(x)) must also exclude x=5.
The domain of f(g(x)) is all real numbers except x=3 and x=5.
How can you use Triangle Congruence to solve real-world problems?
Answers
Answer:
Many pairs of triangles designed into a building, for example as roof ends, would be congruent, so the roof beam and the top edges of the walls are horizontal.
WILL GIVE BRAINLIEST
The difference of two numbers is 2. Their sum is 10. Find the numbers.
Answers
Answer:
6 and 4
Step-by-step explanation:
6 + 4 = 10
6 - 4 = 2
Hope this helped you :)
6 and 4
6-4 = 2
6+4 = 10
They tell you the sum is 10, so think of #'s that make 10:
1,9
2,8
3,7
4,6
5,5
Now, which ones make 2 when subtracted
9-1 = 8
8-2 = 6
7-3 = 4
6-4 = 2
5-5 = 0
Therefore, the answers are 6 and 4
Which line is an asymptote of the function f(x)= -6e^4(x-1) - 2 ?
A. y = 1
B. y = -2
C. y = -6
D. y = 1
Answers
Answer:
i am positive it is B
Step-by-step explanation:
If the area of the triangle with vertices (5,2),(x,4) and (0,3) is 25/2, find x?
Answers
x=7
Pretty Simple.. h h h
The value of the variable 'x' will be 20. Then the third vertice of the triangle is (20, 4).
What is the area of the triangle?The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).
Then the area of the triangle will be
Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|
The vertices of the triangle are given as,
(x₁, y₁) ⇒ (5, 2)
(x₂, y₂) ⇒ (x, 4)
(x₃, y₃) ⇒ (0, 3)
Then the area will be
Area = 1/2[{5 × 4 + x × 3 + 0 × 2} – {2 × x + 4 × 0 + 3 × 5}]
25/2 = 1/2 [20 + 3x – 2x – 15]
25 = [x + 5]
x = 25 – 5
x = 20
The value of the variable 'x' will be 20. Then the third vertice of the triangle is (20, 4).
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Don’t worry about number 4 just tell me the answer to number two
Answers
Answer:
B
Step-by-step explanation:
First, you must combine like terms.
5a - a - a would be 3a.
-6 + 4 would be -2.
3a-2
Answer:
The answer would be B. -a+4+5a-a-6.
You would need to put like terms together. 4 and -6 is -2. -a, 5a, and -a is 3a.
si en la cancha de una escuela se va a colocar 150 sillas en forma rectangular, cuales seran las posibles arreglos de manera que no sobren sillas en ninguna fila
Answers
Answer:
RGRGAEGETG
Step-by-step explanation:
Which best describes the dimensions of a line?
A line has zero dimensions because it represents a location on the coordinate plane.
A line has one dimension because it is made up of all points that extend infinitely in either direction.
A line has two dimensions because it is made up of three noncollinear points.
A line has multiple dimensions depending on how many labeled points it contains.
Answers
Answer:
A line has one dimension because it is made up of all points that extend infinitely in either direction.
Step-by-step explanation:
The correct statement which describes the dimensions of a line is,
''A line has one dimension because it is made up of all points that extend infinitely in either direction.''
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
We have to given that;
To find the dimensions of a line.
We know that;
A line has one dimension because it is made up of all points that extend infinitely in either direction.
Thus, The correct statement which describes the dimensions of a line is,
''A line has one dimension because it is made up of all points that extend infinitely in either direction.''
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help now i will mark brainly
Answers
Answer:
6. 928 R 3
7. 4/6
8. 2/8
Step-by-step explanation:
Need answer asap ...........
Answers
Answer:
25
25
Step-by-step explanation:
3^3 + 10 - 2 * 6
27 + 10 - 12
25
c
10^2 / 2^2
100 / 4
25
Answer:
B.)25
C.) 25
Step-by-step explanation:
B.) 3^3=27
27+10=37
37- 12= 25
_________________________________________
C.) 10^2= 100
100/ 2^2= 25
Brainliest? I am trying to earn a new rank so I can help more people and I would totally appreciate it if you did! Merry Christmas!
What is the quotient of 6 -1/2
Answers
Answer:
-3
Step-by-step explanation:
because quotient means division,
so you divide 6 by -1/2
-1/2 is equal to -0.5
6/-0.5= -3
help me please! is compound interest
Answers
Answer:
7,200
Step-by-step explanation:
Ricky Bobby currently has $500 in his savings account, and figures that he will add $25 per week from his
job. He realizes that he can use the equation
S=25w+500 where S is the amount in savings and w= number of weeks from now.
a. How much will he have saved in 15 weeks
b. When will Ricky Bobby have $1200?
Answers
Ricky Bobby will have saved $875 in 15 weeks and he will have $1200 in 28 weeks.
Firstly solving first part of the question. Here, we need to calculate the savings in 15 weeks. To perform this calculation, we will keep the number of weeks in place of variable w.
Savings = 25×15 + 500
Performing multiplication
Savings = 375 + 500
Performing addition
Savings = $875
Now, solving the second part, which is finding the number of weeks. We will keep the savings amount at place of variable S.
1200 = 25w + 500
25w = 1200 - 500
Performing subtraction
25w = 700
w = 700 ÷ 25
Performing division
w = 28
Therefore, Ricky Bobby will have saved $875 in 15 weeks and he will have $1200 in 28 weeks.
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2 What is the solution set of
|4x - 1|= 3?
Answers
Answer:
Exact Form:
x = 1 , − 1/ 2
Decimal Form:
x = 1 , − 0.5
Step-by-step explanation:
QUICK MATH
pls help I will fail 10th grade
Answers
Answer:
b
Step-by-step explanation:
Please mark brainiest
The health benefits Daisy receives from his employer covers 45% of the total montly premium of $350.00. How much does Daisy have to pay each month?
Answers
Answer:
$192.5
Step-by-step explanation:
1. turn 45% into .45
2. multiply .45 x 350
3. get 157.5 and then subtract 350-157.5
4. answer is 192.5
-9r+10r i have one more pls help me
Answers
Answer:
r
Step-by-step explanation:
10r - 9r = r
pls help me on this
Answers
Answer:
0.3(25)
Step-by-step explanation:
Of = multiply30% = 0.330% of 25 = 0.3(25)I hope this helps!
the unit rate of 2/1 equivalent to the ratio 4/6: 9/12. True or false?
Answers
Answer:
I think true.
Step-by-step explanation:
which of the following is a linear function
Answers
Answer:
The 1st one?
Step-by-step explanation:
Sorry if I'm wrong
7th grade what is the tone, or mood in the beginning of the play? "A christmas carol"
A- Violent and frighting
B- Dark and gloomy
C- Silly and sentimental
D- Loving and festive
Answers
Answer:
C
Step-by-step explanation:
C
PLEASE ANSWER IMMEDIATELY
Simplify the expression -416 - -613 Explain your solution using the additive inverse property.
Answers
Answer: 203
Step-by-step explanation:
-416 + 613
203
The total weight of 50 identical marbles
Answers
Answer:
Is there more parts of the answer?
Answer:
50 * mass per marble
Step-by-step explanation:
Total weight is weight per marble mutiplied by amount of marbles (N*m = M)
What is the value of x in x = inverse of sin(-1/2)?
Answers
Answer:
B. -pi/6
Step-by-step explanation:
From 10 am to 4 pm the temperature changed -36 degrees. If the temperature changed equally for the last 6 hours, How much did it change each hour?
Answers
Answer:
-6 degrees per hour
Step-by-step explanation:
divide -36 by 6(the number of hours) and get -6
Answer:
6 degrees
Step-by-step explanation:
it changed 6 degrees every hour
What is the length of JL?
Answers
As We can see that point J is on (-2,5) and L is on (-2,-2)
So we know that distance cannot be in negative, thus
Distance between J and L =5+2=7 units
JL=7
Mrs.jones waters the plants on her porch every 5 days. She waters the vegetable garden every 2 days. If she waters them both today, how many days will pass before she will water both of them on the same day again?
Answers
the answer is 10. if you take the lcm of 5 and 2 you should get it.